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Satellites

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Question

Two satellites of masses m1 and m2 (m1 > m2) are revolving round the earth in circular orbits of radii r1 and r2 (r1 > r2) respectively. Which of the following statements is true regarding their speeds v1 and v2 ?

A

v1 = v2

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B

v1 < v2

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C

v1 > v2

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D

(v1/r1) = (v2/r2)

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Solution

The correct option is A v1 < v2
We know that orbital velocity, v is given by $\sqrt{} (G M / r) .$ As orbital velocity is independent of mass of
body so orbital velocity, v is inversely proportional to $\sqrt{} r .$
So, the correct expression is $v_{2} > v_{1}$ as it given that $r_{1} > r_{2} .$

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